Have a look at the SMSL D1 DAC, people are saying it's great sound for low cost (
80 euros).
You can pair that with a decent quality low cost TPA3255 amp.
There are MANY of them and most of them even super cheap ones sound surprisingly good.
For example the BRU5 amp costs only about $30 and sounds fine esp given the price.
I mention that one only because I own it (the TPA3244 version not TPA3255)
I'm using via my PC and a $20 USB dongle DAC via RCA-inputs, so I know how it sounds... lovely sound considering only $50 total price.
But there are other brand TPA3255 amps more well known and reviewed for around 70 euros to 100 euros, as you probably know (eg Douk A5).
Keep in mind also that I have very large DIY loudspeakers with 96db/1watt sensitivity and a big titanium horn tweeter.
If my cheap $50 front end was bright or grainy (not smooth) or bad sounding, I would definitely hear it. The speakers would expose all the gremlins.
But it sounds very nice and smooth, surprisingly so, even if it's not the most "3D" soundstage/imaging.
So with the above your total cost for DAC + Amp would be from 110 to 150 euros and you can save money for upgrading your speakers, which is the most important thing to spend your budget on.
The SMSL D1 + Douk A5 I bet would make an awesome combo for about 160 euros.
I have the D1 on order so will know more
personally/first-hand later. ;-) cheers.